bdgraph.sim {BDgraph}

Graph data simulation

Description

Simulating multivariate distributions with different types of underlying graph structures, including "random", "cluster", "smallworld", "scale-free", "lattice", "hub", "star", "circle", "AR(1)", and "AR(2)". Based on the underlying graph structure, the function generates different types of multivariate data, including "Gaussian", "non-Gaussian", "categorical", "pois" (Poisson), "nbinom" (negative binomial), "dweibull" (discrete Weibull), "binary", "t" (t-distribution), "alternative-t", or "mixed" data. This function can be used also for simulating only graphs by setting the option n=0 (default).

Usage

bdgraph.sim( p = 10, graph = "random", n = 0, type = "Gaussian", prob = 0.2, 
             size = NULL, mean = 0, class = NULL, cut = 4, b = 3,
             D = diag( p ), K = NULL, sigma = NULL, 
             q = exp(-1), beta = 1, vis = FALSE, rewire = 0.05,
             range.mu = c( 3, 5 ), range.dispersion = c( 0.01, 0.1 ), nu = 1 )

Arguments

p

number of variables (nodes).

graph

graph structure with options "random", "cluster", "smallworld", "scale-free", "lattice", "hub", "star", "circle", "AR(1)", and "AR(2)". It could also be an adjacency matrix corresponding to a graph structure (an upper triangular matrix in which g_{ij}=1 if there is a link between nodes i and j, otherwise g_{ij}=0).

n

number of samples required. Note that for the case n = 0, only the graph is generated.

type

type of data with options "Gaussian" (default), "non-Gaussian", "categorical", "pois", "nbinom", "dweibull", "binary", "mixed", "t", and "alternative-t". For the option "Gaussian", data are generated from a multivariate normal distribution. For the option "non-Gaussian", data are transfered from a multivariate normal distribution to a continuous multivariate non-Gaussian distribution via Exponential marginals. For the option "categorical", data are transfered from a multivariate normal distribution to multivariate 'categorical' data. For the option "pois", data are transfered from a multivariate normal distribution to a multivariate Poisson distribution. For the option "nbinom", data are transfered from a multivariate normal distribution to a multivariate Negative Binomial distribution. For the option "dweibull", data are transfered from a multivariate normal distribution to a multivariate discrete Weibull distribution with parameters q and beta. For the option "binary", data are generated directly from the joint distribution, in this case p must be less than 17. For the option "mixed", data are transfered from a multivariate normal distribution to a mixture of 'categorical', 'non-Gaussian', 'binary' and 'Gaussian', respectively.

prob

if graph = "random", it is the probability that a pair of nodes has a link.

size

number of links in the true graph (graph size).

mean

vector specifying the mean of the variables.

class

if graph = "cluster", it is the number of classes.

cut

if type = "categorical", it is the number of categories for simulating 'categorical' data.

b

degree of freedom for G-Wishart distribution, W_G(b, D).

D

positive definite (p \times p) "scale" matrix for G-Wishart distribution, W_G(b, D). The default is an identity matrix.

K

if graph = "fixed", it is a positive-definite symmetric matrix, corresponding to the true precision matrix.

sigma

if graph = "fixed", it is a positive-definite symmetric matrix corresponding to the true covariance matrix.

q, beta

if type = "dweibull", they are the parameters of the discrete Weibull distribution with density

p( x, q, \beta ) = q^{x^{\beta}}-q^{(x+1)^{\beta}}, \quad \forall x = \{ 0, 1, 2, \ldots \}.

They can be given either as a vector of length p or as an (n \times p) matrix, e.g. if covariates are available and a regression model is used.

vis

visualize the true graph structure.

rewire

rewiring probability for smallworld network. Must be between 0 and 1.

range.mu, range.dispersion

if type = "nbinom", vector with two elements specifying the range of parameters for the Negative Binomial distribution.

nu

if type = "t" or "alternative-t", it is the parameter of the t distribution with density.

Value

An object with S3 class "sim" is returned:

data

generated data as an (n \times p) matrix.

sigma

covariance matrix of the generated data.

K

precision matrix of the generated data.

G

adjacency matrix corresponding to the true graph structure.

Author(s)

Reza Mohammadi [e-mail], Pariya Behrouzi, Veronica Vinciotti, Ernst Wit, and Alexander Christensen

References

Mohammadi, R. and Wit, E. C. (2019). BDgraph: An R Package for Bayesian Structure Learning in Graphical Models, Journal of Statistical Software, 89(3):1-30, doi:10.18637/jss.v089.i03

See Also

graph.sim, bdgraph, bdgraph.mpl

Examples

## Not run: 
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( p = 10, n = 50, prob = 0.3, vis = TRUE )

print( data.sim )
     
# Generating multivariate normal data from a 'hub' graph
data.sim <- bdgraph.sim( p = 6, n = 3, graph = "hub", vis = FALSE )

round( data.sim $ data, 2 )
     
# Generating mixed data from a 'hub' graph 
data.sim <- bdgraph.sim( p = 8, n = 10, graph = "hub", type = "mixed" )

round( data.sim $ data, 2 )

# Generating only a 'scale-free' graph (with no data) 
graph.sim <- bdgraph.sim( p = 8, graph = "scale-free" )

plot( graph.sim )

graph.sim $ G

## End(Not run)